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A 23 Measuring the Electromotive Force (EMF)
Task:
I) Determine the electromotive force of the following galvanic cells:
A.) Cu / 1.0 M CuSO 4 / sat. KCl – sol. / 1.0 M ZnSO 4 / Zn B.) Cu / 1.0 M CuSO 4 / sat. KCl – sol. / 0.1 M CuSO 4 / Cu C.) Zn / 1.0 M ZnSO 4 / sat. KCl – sol. / 0.1 M ZnSO 4 / Zn D.) Cu / 1,0 M CuSO 4 / sat. KCl – sol. / AgCl / Ag E.) Zn / 1.0 M ZnSO 4 / sat. KCl – sol. / AgCl / Ag F.) Cu / 0.1 M CuSO 4 / sat. KCl – sol. / 0.1 M ZnSO 4 / Zn
II) Determine the solubility product of AgCl.
III) Determine, from the temperature dependency of the EMF of the galvanic cell F, the reaction enthalpy and the reaction entropy.
Basics:
A galvanic cell, made up of two half-cells, allows us to observe the work done by a chemical reaction as electrical energy. If, during the measurement process, a negligible current is flowing, then a galvanic cell operates reversible (this can also be obtained with the use of a high-ohm voltmeter, where the typical input current is < 10-9^ A). The electrical work correlates to the maximum producible work or the free energy of a corresponding reaction. The potential-building process in a metal electrode, which is immersed in a salt solution of the same metal (half-cell), is based upon the attempt of the metal atoms to reach equilibrium with the ions in the solution.
There are differing ways to explain this process, which all lead to the Nernst-equation:
∆ ߮ൌ ∆߮ ^ െ ோ ∙்݈݊௭ ∙ி ܽ∏^ (^) ௩^ (1)
߮∆ : Potential difference
߮∆ : Standard potential difference
R: Gas constant
T: Temperature
z: Transferred charge per formula unit of the reaction
F: Faraday constant
ܽ : Activity of the species i
ݒ: Stoichiometric factor of the species i
Generally, the EMF is measured at constant pressure. The work
performed corresponds to the free enthalpy ∆G:
∆ ܩൌ െ ݖ∙ ܨ∙ ܧൌ െ ݖ∙ ܨ∙ ∆߮ (2)
E: EMF
The use of equation (2) should be illustrated using the Daniell- Element as an example: Metallic Copper immersed in an aqueous CuSO 4 solution, metallic Zink immersed in a ZnSO 4 solution. The solutions are separated by a porous separator (diaphragm). The overall reaction is as follows:
Zn + CuSO 4 → Cu+ ZnSO 4
߮௨ ௨⁄ మశ߮ൌ ௨ ௨^ ⁄ మశ ோ்݈݊௭ி
ೠమశ ೠ (6a)
߮ ⁄ మశ ߮ൌ (^) ^ ⁄ మశ ோ்݈݊௭ி
ೋమశ (^) ೋ^ (6b)
Since the activity of a pure metal is not dependant on the solution, the corresponding/equivalent value can be added to the standard potential:
߮ ௨ ௨⁄ మశ߮ൌ (^) ௨ ௨^ ⁄ మశ ோ்݈ܽ݊௭ி ௨ మశ (7a)
߮ ⁄ మశ ߮ൌ (^) ^ ⁄ మశ ோ்݈ܽ݊௭ி మశ (7b)
Since the activity of single ions cannot be measured, we define the mean ionic activity coefficient of a salt Ax By as:
ߛേሺ௫ା௬ሻ^ ߛ ൌା௫^ ିߛ ௬^ (8)
and the mean ionic activity as:
ܽ േሺ௫ା௬ሻ^ ܽൌ (^) ାିܽ௫^ ௬^ (9)
For 1:1 electrolytes this gives:
ܽ േ ܽൌ (^) ା ିܽൌ ߛܥ ൌേ (10)
where C is the molar concentration of the salt.
Now it is possible to calculate the activity coefficient from EMF measurements with known standard potentials. The standard potentials can be determined at very low concentrations as the Debye-Hückel Limiting Law sufficiently describes the activity coefficient in this range. Thus, one obtains the following equation for the Daniell- element:
߮ሺ ൌ ܧ^ ௨^ ߮െ (^) ^ ሻ െ ோ்௭ி ݈݊∙
ೋೄೀర ∙ఊ (^) േೋೄೀర ೠೄೀర ∙ఊ (^) േೠೄೀర^ (11)
Standard potentials are referred to T = 298.16 K and p = 1 bar at a
hypothetical concentration of 1 mol/l. The standard hydrogen electrode is used as a reference, where its potential is fixed at 0 V. In practice, other reference electrodes would be used instead of the difficult to use hydrogen electrode.
Whereas, up until now, only half-cells with differing electrodes have been dealt with, it is also possible to have electrodes of the same material but differing concentration. For these “concentration cells”, analogous consideration gives us:
ൌ ܧ ோ்௭ி ݈݊∙
భೠೄೀర ∙ఊ భേೠೄೀర మೠೄೀర ∙ఊ మേೠೄೀర^ (12)
If there is only a slight difference in concentration, the activity coefficients will be almost equal, giving:
ൌ ܧ ோ்௭ி ݈݊∙ ^
భೠೄೀర మೠೄೀర^ (13)
For the experimental series in Task III, glass apparatus which are closed at their lower end with a frit are used. The salt bridge is a temperature controlled, double walled beaker filled with saturated potassium chloride solution in which the two half-cells are inserted. The insertion of the electrodes – which are connected to the multimeter – is the starting point of the measurement. For the temperature dependant experiments, data will be collected for ca. 15 minutes at 25°C then, without pausing the experiment, the thermostat will be set to 50°C. The experiment will be continued until the temperature has reached the preset final value. The EMF is recorded at regular temperature intervals.
Data Analysis:
All results will be discussed and compared to the literature!
- From the measured EMF values of the cells A.) and D.) and A.) and E.) respectively, calculate the EMF of the cells E.) and D.) respectively. Compare the results with the measured values.
- Reference the electrode potential of Zn / Zn2+^ and Cu / Cu2+^ to the standard hydrogen electrode and order them in an electrochemical series.
- Calculate the EMF of the cells B.) and C.) using equation (13). Compare the results with the measured values.
- Repeat the calculation with equation (12) using the activity coefficient (ߛേ௨ௌைଵெ^ ర ൌ 0.041, ߛേ௨ௌை.ଵெ^ ర ൌ 0.149. The values for ZnSO 4 can be obtained from the literature). Discuss any potential discrepancies.
- Calculate the silver ion concentration from the stoichiometry of the chloride ion concentration and the measured EMF.
- Using the Gibbs-Helmholtz equation, calculate the enthalpy and entropy of the reaction at room temperature. How large is the effective work ∆G for this reversible reaction process? What is the efficiency of the Daniell-element?
What you should know:
- Error sources in EMF measurements
- Second order electrodes, Hydrogen electrodes
- Diffusion potential
- Overpotential
- Redox potential
- Electrochemical series
- Nernst Equation
- Solubility product
- Chemical and electrochemical equilibrium conditions
- Temperature dependency of EMF
Extra Question:
Derive the Nernst equation using the electrochemical equilibrium conditions.
